Matrix equation system with orthogonal matrices

79 Views Asked by At

$T_1,T_2$ are unknown orthogonal matrices $3\times3$ with determinant 1, $v_i,u_i$ are known vectors $3\times1$.

How can i elegantly solve this ?

$T_1v_1=T_2u_1$

$T_1v_2=u_2$

$T_2v_3=u_3$